Origins of algebra

what I want to do in this video is think about the origins of algebra the origins of algebra and the word especially an association with the ideas that algebra now represents comes from comes from this book or actually this is a page of the book right over there the English translation for the title of this book is the compendium calculation by completion and balancing and it was written by a Persian mathematician who lived in Baghdad in in I believe is was it was in the 8th or 9th century I believe it was actually 820 ad when he wrote this book ad and algebra is the Arabic word that here's the actual the title that he gave to it which is the Arabic title algebra means restoration or completion restoration restoration or completion completion and he associated in his book with a very specific operation really taking from one side something from one side of an equation to another side of an equation but we can actually see it right over here and I don't know Arabic but I actually do know some languages that seems to have borrowed a little bit from Arabic or maybe it went the other way around but this says al-kitab and III know just enough or do and Hindi to understand a good Indian movie but al kitab kitab means book so this part is book book o Muktha tsar i I well I think that means compendium or compendious and that seems like that fee his saab his saab means calculation in hindi urdu so this is calculation calculation al Jabar this is this is the root this is the famous algebra this is where it shows up so this is for completion you could view that as completion completion and then while all MOOC habla and that means essentially balancing balancing completion and balancing so if we wanted to translate and I know this isn't a video on translating Arabic but the book the book the the book I guess this is saying compendious on on calculation and complete calculation by completion and balancing is the rough translation right over there but that is the source of the word algebra and this is a very very very important book not just because it was the first use of the word algebra but many people viewed this this book as the first time that algebra took a lot of it's a lot of it's a lot of its modern a lot of its modern took on many of its modern ideas ideas of balancing an equation the abstract problem itself not trying to do one-off problems here or there but I'll acquire is me was not the first person and just to get an idea of where all of this is happening so he was hanging out in Baghdad so this is and this part of the world shows up a lot in the history of algebra but he was hanging out right there in around the 8th or 9th century so let me let me draw a little timeline here just so we can appreciate everything so that is timeline and then whether or not you do are religious most of our modern dates are dependent on the birth of Jesus so I will put so that is right there I'll put a cross over there to signify that when we want to be non-religious we say Common Era before the Common Era when we want to be religious we say ad which means in the year of our Lord a node I don't know the Latin anno domini I believe year of our Lord and then when we want to and in the religious context instead of saying before Common Era we say before Christ BC but either way either way so this is 1,000 in the Common Era this is 2,000 in the Common Era and obviously we are sitting at least when I'm making this video I'm sitting right about there and then this is 1,000 before the Common Era and this is 2,000 before the Common Era so the first traces and I'm skipping out and and really it's just what we can find I'm sure if we were able to dig more we might be able to find other evidence of different civilizations and different people stumbling on many of the ideas in algebra but our first records of people really exploring the ideas that are hit upon an algebra come from ancient Babylon around 2,000 years before the Common Era before Christ so right around right around right around there are we there stone tablets where it looks like people were exploring some of the fundamental I of algebra they weren't using the same symbols they weren't using the same ways of representing the numbers but it was algebra that they were working on and that was once again in this part of the world Babylon was right about right about there and Babylon it's kind of kept the tradition of Sumeria this holy this whole region was called Mesopotamia Greek for between two rivers but that's the first traces of people that we know of that where people were starting to do what we would call real real algebra and then you fast forward and and I I'm sure we're missing and I'm sure even our historians don't know all of the different the different instances of people using algebra but kind of the law the the major the major contributions to algebra we saw it here in Babylon 2,000 years ago and then if we fast forward to about 200 to 300 AD so right over there you have a Greek gentleman who lived in Alexandria so this is this is Greece right over here but he lived in Alexandria which at the time was part of the Roman Empire so Alexandria is right over here and he was a gentleman by the name of Diophantus or Diophantus or i don't know how to pronounce it die o diophantus and he is sometimes credited with being the father of algebra and it's debatable whether it's Diophantus or whether it's all queries me i'll curry's me who kind of started using these terms of balancing equations and talking about math in a pure way while diophantus was more focused on particular problems and both of them were kind of beat to the punch by by the Babylonians although they all did contribute in their own way it's not like they were just copying what the Babylonians did they had their own unique contributions to what we now consider algebra but many especially Western historians associate Diophantus as the father of algebra and now I'll charisma is sometimes what other people would argue as the father of algebra so he made significant contributions and if you go to 600 ad so if you got about 600 ad another famous mathematician in the in the history of algebra was Brahma Gupta in India Brahma Gupta in India so obviously and actually I don't know where in India he lived I should look that up but roughly roughly in that part of the world and he also made significant contributions and then of course you have and then you have alcaraz me who shows up right about right right there i'll quar is me and he's the the gentleman that definitely we credit with the name algebra comes from arabic for restoration and some people also consider him to be if not the father found a role too some people say he is the father he is one of the fathers of algebra because he really started to think about algebra in the abstract sense devoid of some specific problems and a lot of the way that a modern mathematician would would start to think about the field